Is this normal?
 

This new leaf is cutting through the older leaf. Anyone ever had this happen?

Hi Unique562
I had this happening last year with a Phal. The new leaf cut the previous almost one third of the longitudinal extension while developing.

Stupid me tried to pull the leaf through and broke the new leaf off. I'm so mad. Anyways does that mean the plant will die or keep growing?

Presuming your plant is a Phalaenopsis, damaging the crown is not a good thing, especially breaking off the new leaf. The crown is the heart of that orchid. It normally has some spare meristems that allow the plant to form a new shoot from another point, but this is not assured. Good luck with your plant!